Question

question
factor.
$x^2 - 3x - 28$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-28\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)). Let's list the factor pairs of \(28\): \(1\) and \(28\), \(2\) and \(14\), \(4\) and \(7\). We need one positive and one negative number since their product is negative. We find that \(4\) and \(-7\) work because \(4\times(-7)= -28\) and \(4 + (-7)= -3\).

Step2: Factor the quadratic

Using the numbers we found, we can factor the quadratic \(x^{2}-3x - 28\) as \((x + 4)(x - 7)\). We check by expanding: \((x + 4)(x - 7)=x^{2}-7x + 4x - 28=x^{2}-3x - 28\), which matches the original expression.

Answer:

\((x + 4)(x - 7)\)